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Title: Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions
Authors: Ilic, M.
Liu, F.
Turner, I.
Anh, V.
Keywords: Fractional Diffusion
Anomalous Diffusion
Non-Homogeneous Boundary Conditions
Numerical Approximation
Issue Date: 2006
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 9, No 4, (2006), 333p-349p
Abstract: In this paper, a space fractional diffusion equation (SFDE) with nonhomogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally efficient and accurate method for solving SFDE.
Description: 2000 Mathematics Subject Classification: 26A33 (primary), 35S15
ISSN: 1311-0454
Appears in Collections:2006

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